The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  0  2  0  0  2  X  X  1  1
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2  X  2  X  X  0  2  2  0  2  2 X+2
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  X  2  0  X  2  X  X X+2  X  2  X
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0  2  X  0  2  X  0 X+2  2  0 X+2 X+2
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  2  2
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  0  2  2  2  2  0  2  0  0  2
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  2  2  2  0  2  0  0  2  0  2  0

generates a code of length 28 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+38x^21+117x^22+134x^23+184x^24+328x^25+463x^26+540x^27+538x^28+516x^29+460x^30+312x^31+157x^32+136x^33+104x^34+36x^35+14x^36+6x^37+7x^38+2x^39+2x^40+1x^42

The gray image is a code over GF(2) with n=112, k=12 and d=42.
This code was found by Heurico 1.16 in 0.375 seconds.